Neutral seventh

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Neutral seventh
Inverse neutral second
Other names -
Abbreviation n7
Semitones ~10½
Interval class ~1½
Just interval 11:6,[1] 64:35,[2] or 24:13
Equal temperament 1000 or 1100
Just intonation 1049, 1045, or 1061
Neutral seventh on C About this sound Play .

A neutral seventh is a musical interval wider than a minor seventh About this sound play  but narrower than a major seventh About this sound play . Four distinct intervals may be termed neutral sevenths:

  • A septimal neutral seventh About this sound play  has a ratio of 64:35 or about 1045 cents.
  • The just undecimal neutral seventh has a ratio of 11:6 between the frequencies of the two tones,[3] or about 1049 cents About this sound play . Alternately, 13:7[3] or about 1071.7 cents.
  • A tridecimal neutral seventh About this sound play  has a ratio of 24:13 between the frequencies of the two tones, or about 1061 cents. This is the largest neutral seventh, and occurs infrequently in music, as little music utilizes the 13th harmonic.
  • An equal-tempered neutral seventh About this sound play  is characterized by a difference in 1050 cents between the two tones, a hair larger than the 11:6 ratio, and exactly half of an equal-tempered major thirteenth (octave plus major sixth).

These intervals are all within about 12 cents and are difficult for most people to distinguish. Neutral sevenths are roughly a quarter tone sharp from 12 equal temperament minor sevenths and a quarter tone flat from 12-ET major sevenths. In just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate just intonation, the intervals are closer together.

A neutral seventh can be formed by stacking a neutral third together with a perfect fifth. Based on its positioning in the harmonic series, the undecimal neutral third implies a root one perfect fifth below the lower of the two notes.

See also[edit]


  1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0-8247-4714-3. 21/4-tone, undecimal neutral seventh.
  2. ^ Haluska (2003), p.?. Septimal neutral seventh.
  3. ^ a b Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0-89579-507-8.